Almost a month after Boeing finished a software update for its 737 Max aircraft, it's still unclear when the plane will return to service as pressure on the aerospace manufacturer builds.

The 737 Max has been grounded in much of the world since March following two deadly crashes that killed nearly 350 people. Technology designed to prevent the aircraft from stalling has come under scrutiny, as it activated during both crashes due to false sensor readings and pushed the planes downward at too steep of an angle.

On May 16 , Boeing finished a software update for the 737 Max that the Federal Aviation Administration (FAA) must approve before the aircraft can resume commercial flights in the US, but neither Boeing nor the FAA has given a clear, public indication of when the approval process may end.

According to a Bloomberg report from May, Boeing told one of its biggest 737 Max customers, SpiceJet, that the aircraft would likely be flying again by July, but Boeing CEO Dennis Muilenburg declined to offer a similarly concrete prediction during a June 3 interview with CNBC .

When asked if he believed the 737 Max would resume flight before the end of the year, Muilenburg said, "I do, but again, I can't give you the specific timeline on it."

In response to a question from Business Insider about when the 737 Max might return to service, a Boeing representative did not give a timeline, but said the company is working to address requests from the FAA.

"Boeing is now providing additional information to address Federal Aviation Administration (FAA) requests that include detail on how pilots interact with the airplane controls and displays in different flight scenarios," the representative said. "Once the requests are addressed, Boeing will work with the FAA to schedule its certification test flight and submit final certification documentation."

The FAA did not immediately respond to Business Insider's request for comment.

Public uncertainty around the 737 Max's return comes as Boeing faces mounting pressure from lawsuits and investigations related to the aircraft, as well as potential issues with the wings of both 737 Max and 737 Next Generation planes.

The company also faces the prospect of continued financial fallout from the 737 Max. In April, Boeing said decreased production stemming from the 737 Max bans had cost it $1 billion during the first quarter of 2019. The company made $22.9 billion in revenue during the quarter, a 2% decrease from the first quarter in 2018, and $2 billion in adjusted profits, a 21% decrease from the first quarter in 2018.